Chapter 8 - Geometry - 8.8 Pythagorean Theorem - 8.8 Exercises - Page 593: 43

The diagonal brace of the rectangular gate is $\approx 5.7$ ft.

Let $H =$ hypotenuse of the triangle / diagonal brace of the gate $a^{2} + b^{2} = c^{2}$ $(4.5)^{2} + (3.5)^{2} = H^{2}$ $20.25 + 12.25 = H^{2}$ $32.5 = H^{2}$ $H = \sqrt 32.5$ $H = 5.701...$ $H \approx 5.7$ ft